Cremona's table of elliptic curves

550 = 2 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	550f	Isogeny class
Conductor	550	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-720896000000000 = -1 · 225 · 59 · 11	Discriminant
Eigenvalues	2+  1 5- -3 11- -4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-758201,254051548]	[a1,a2,a3,a4,a6]
Generators	[502:-189:1]	Generators of the group modulo torsion
j	-24680042791780949/369098752	j-invariant
L	1.6665638072801	L(r)(E,1)/r!
Ω	0.46396462077251	Real period
R	1.7960031138853	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4400w3 17600w3 4950bq3 550k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550f3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	1	-	-3	-	-4	-3	-5	-4	5	7	7	-8	6	-8	-9	0	-13	12	-3	6	0	-4	-15	12

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Quadratic twists for elliptic curve 550f3

-4	8	-3	5	-7	-11	13
4400w3	17600w3	4950bq3	550k3	26950bm3	6050bj3	92950cp3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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